Software sensor for microalgae culture: Theoretical development, numerical solutions and real time implementations

This chapter describes a fixed-time convergent step-by-step high order sliding mode observer for a certain type of microalgae culture system. The observer was developed using a finite-time hierarchical structure based on a modified super twisting algorithm. The modification included nonlinear gains of the output error that were used to prove uniform convergence of the estimation error. An energetic function similar to a Lyapunov one was used for proving the convergence between the observer and the bioreactor variables. A non-smooth analysis was proposed to prove the fixed-time convergence of the observer states to the microalgae culture variables. The observer was tested to solve the state estimation problem of an aerobic reaction governed by the Droop model described by the time evolution of biomass, substrate and nitrogen quota. The former variable was used as the output information because it is feasible to measure it on-line by regular sensors. Numerical simulations showed the superior behavior of this observer compared to the one having linear output error injection terms (high-gain type) and one having an output injection obtaining first order sliding mode structure.